/*
 * Copyright 2010-2012 Susanta Tewari. <freecode4susant@users.sourceforge.net>
 *
 * This program is free software: you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation, either version 3 of the License, or
 * (at your option) any later version.
 *
 * This program is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program.  If not, see <http://www.gnu.org/licenses/>.
 */

package bd.org.apache.commons.math.linear;

/**
 * Interface handling decomposition algorithms that can solve A &times; X = B.
 * <p>Decomposition algorithms decompose an A matrix has a product of several specific
 * matrices from which they can solve A &times; X = B in least squares sense: they find X
 * such that ||A &times; X - B|| is minimal.</p>
 * <p>Some solvers like {@link LUDecomposition} can only find the solution for
 * square matrices and when the solution is an exact linear solution, i.e. when
 * ||A &times; X - B|| is exactly 0. Other solvers can also find solutions
 * with non-square matrix A and with non-null minimal norm. If an exact linear
 * solution exists it is also the minimal norm solution.</p>
 *
 * @version $Id: DecompositionSolver.java 1244107 2012-02-14 16:17:55Z erans $
 * @since 2.0
 */
public interface DecompositionSolver {

    /**
     * Solve the linear equation A &times; X = B for matrices A.
     * <p>The A matrix is implicit, it is provided by the underlying
     * decomposition algorithm.</p>
     *
     * @param b right-hand side of the equation A &times; X = B
     * @return a vector X that minimizes the two norm of A &times; X - B
     * @throws org.apache.commons.math3.exception.DimensionMismatchException if the matrices dimensions do not match.
     * @throws SingularMatrixException if the decomposed matrix is singular.
     */
    RealVector solve(final RealVector b);


    /**
     * Solve the linear equation A &times; X = B for matrices A.
     * <p>The A matrix is implicit, it is provided by the underlying
     * decomposition algorithm.</p>
     *
     * @param b right-hand side of the equation A &times; X = B
     * @return a matrix X that minimizes the two norm of A &times; X - B
     * @throws org.apache.commons.math3.exception.DimensionMismatchException if the matrices dimensions do not match.
     * @throws SingularMatrixException if the decomposed matrix is singular.
     */
    RealMatrix solve(final RealMatrix b);


    /**
     * Check if the decomposed matrix is non-singular.
     *
     * @return true if the decomposed matrix is non-singular.
     */
    boolean isNonSingular();


    /**
     * Get the inverse (or pseudo-inverse) of the decomposed matrix.
     *
     * @return inverse matrix
     * @throws SingularMatrixException if the decomposed matrix is singular.
     */
    RealMatrix getInverse();
}
